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Questions tagged [geometric-progressions]

A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence

A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. This can be useful when evaluating (in)finite series or determining a closed form for a recurrence relation.

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How does this equation work?

I had asked this question here Geometric Progression: How to solve for $n$ in the following equation $\frac {5^n-1}4 \equiv 2 \pmod 7$ and accepted solution has conclusion $$\frac{5^n-1}4\equiv 2\pmod 7\iff n\equiv 4\pmod 6$$ I wanted to understand…
Vishal Anand
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Geometric Progression: How to solve for $n$ in the following equation $\frac {5^n-1}4 \equiv 2 \pmod 7$

Solve $$\frac {5^n-1}4 \equiv 2 \pmod 7$$ How to find the minimum value of $n$ that can satisfy above equation?
Vishal Anand
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Sum of members of Geometric progression

They want me to find the 3 members of a decreasing geometric progression. And I am given that let them be $a,b,c$ $a+b+c=14$ and that $a^2+b^2+c^2=84$ I tried to express everything with the first so $a+a.q+a.q^2=14$…
yolo expectz
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Calculating annuity payments with payment inflation and final value of zero

I am trying to calculate the total amount required in a retirement account given $S$: starting amount $P$: first year payment $i$: decimal inflation rate $I$: $1 + i$ $y$: decimal yield on balance $Y$: $1 + y$ $N$: number of years of retirement If…
Ralph
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Geometric Progression prove the answer

Geometric sequence has first term $a$ and last term $l$ and the sum of all these terms is $S$. Prove that the common ratio of the sequence is $\frac{S-a}{S-l}$. How to include the answer with $S$?
Yvonne Y33
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Common ratio of a geometric progression

In a geometric progression containing $6$ terms, the first term is $2$ and the sum of $6$ terms is $728$. What is the common ratio?
Achari S Ganesha
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Geometric progression having the first and last values and the number of steps

Here's the task at hand: I have the first and last values (a range from 0 to 100) I have the number of steps (20) I need to find values for all 20 steps So, a simple arithmetic progression would be to use the difference of 5 for each step.…
artooras
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I'm not getting the correct sum for this geometric progression word problem.

This is another question my teacher asked to do as homework. I've been getting the sum for this word problem.Here's the word problem: A man on a diet loses 1.5% of his weight during each week. (a) If he initially weighs 150kg, write down his body…
AugieJavax98
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I'm having trouble getting the number of terms for the sum of this geometric progression.

This question has been making me mad all day! It's in a advanced maths text book and my teacher asked us to do it for homework. Here's the question: How many terms of the sequence 4, 3, 2.25, ... can you add before the sum exceeds 12? Here's my…
AugieJavax98
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How can solve this problem of geometric-progression?

A city has $29,524$ inhabitants. One listen about news. After an hour, this man announces to three of his neighbors. In one hour, each neighbors announces to three neighbors. x <- Starter …
Splitzer
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How can I find the first term of this geometric progression?

All the terms in this geometric progression are positives. Given the fifth term is four times that of the third term and the second term is $\frac 18$. So, we have $T_2 = \frac18$ And let say that $T_3 = x$ so $T_5 = 4x$ So the common ratio would…
Valent Pierce
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Ratio of odd terms of a geometric progressions

question:express the ratio of the sum of the squares of the odd number of terms of a GP to the sum of those terms as a polynomial of the common ratio of the GP My try:I have first let a GP with $2n+1$ terms $a, ar, ar^2....ar^{2n}$ then odd terms…
Kartik Watwani
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If $a, b, c, d$ are in G.P., prove that they are in the same place as if they were in a different place.

If $a, b, c, d$ are in G.P., prove that $\left(a^{2}+b^{2}\right),\left(b^{2}+c^{2}\right),\left(c^{2}+d^{2}\right)$ are in G.P. And in general, If $a, b, c, d$ are in G.P., prove…
user845875
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Find the common ratio of the progression.

A geometric progression has 625 as the first term. The product of its first 3 terms is equal to the product of its first 6 terms. Find the common ratio of the progression.
Rodrigo Vu
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How to calculate the sum of the series?

Given $p$,$x$ and $n$ , I have to calculate(find a closed form for the following four series) : 1) $p^1+p^2+p^3+.......+p^n$ 2) $p^1(p^1-1) +p^2(p^2-1)+p^3(p^3-1)+.......+p^n(p^n-1)$ 3) $p^1(p^1-1)(p^1-2)(p^1-3)…
Sanghty reqwwe
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